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Evidence for Ferroelectricity in Iv-Vi Compounds G EVIDENCE FOR FERROELECTRICITY IN IV-VI COMPOUNDS G. Pawley To cite this version: G. Pawley. EVIDENCE FOR FERROELECTRICITY IN IV-VI COMPOUNDS. Journal de Physique Colloques, 1968, 29 (C4), pp.C4-145-C4-150. 10.1051/jphyscol:1968423. jpa-00213627 HAL Id: jpa-00213627 https://hal.archives-ouvertes.fr/jpa-00213627 Submitted on 1 Jan 1968 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE Colloque C 4, supplkment au no 11-12, Tome 29, Novembre-Dkcembre 1968, page C 4 - 145 EVIDENCE FOR FERROELECTRICITY IN IV-VI COMPOUNDS Department of Natural Philosophy - The University, Edinburgh, Scotland Rbum6. - Parce que les mkthodes habituelles servant h ktablir le caractkre ferroklectrique des cristaux ne sont pas applicables au cas de corps de haute conductivitk, on doit alors introduire d'autres moyens basks sur d'autres propriktks ferroklectriques. L'analyse de la structure cristalline peut fournir un modile montrant la possibilitk de polarisation reversible, mais une preuve plus convaincante peut venir de l'ktude de la dynamique du cristal. La diffusion inklastique cohbente des neutrons donne les frkquences des modes normaux du cristal et la variation en tempkrature de certains modes peut indiquer la ferroklectricite ou I'antiferrokkctricite. Des exemples de ces ph6- nomines sont prksentts pour SnTe, suggkrant, de plus, que les solutions solides de SnTe avec GeTe forment un vaste domaine oh existe le caract6re ferroklectrique. Abstract. - Because the usual methods for establishing ferroelectricity in crystals are not possible for crystals with high conductivities, other ways must be introduced based on other ferroelectric prop&rties. ~nalysisofthe crystal structure can provide a model showing the possibility of reversible polarisation, but more convincing evidence can come from the study of the dynamics of the crystal. Neutron inelastic coherent scattering yields the frequencies of the normal modes of the crystal, and the temperature dependence of certain modes can point to ferroelectricity or antiferroelectricity. Examples of both these phenomena are presented for SnTe, suggesting moreover that the solid solutions of SnTe with GeTe form a wide ferroelectric range. 1. Introduction. - The standard methods of could be classed as ferroelectric. We wish to extend establishing the existence of ferroeIectricity in a the classification so as to include those semi- crystalline substance have until recently been sufficient conducting (or even metallic) crystals which display to remove any doubt in most cases [I]. Ferroelectricity other properties indicative of ferroelectricity. Here is confirmed by hysteresis in the E-D (field- we turn to Cochran's [2] theory of ferroelectricity displacement) relationship. The crystal is polarised and show, with SrTiO, as an example, the permanently in a certain direction, but this polarisation relationship between the dielectric phenomena and can be reversed by application of a large enough field, the variation of a certain mode of vibration of the known as the coercive field. The resulting crystal crystal. structure (at least for any case of interest here) is A basic relation between certain modes of vibration related to the initial structure by centrosymmetric of a crystal and its dielectric constants has been proved inversion. Clearly this means that the ferroelectric by Lyddane, Sachs and Teller 131. crystal structure must be acentric. The ferroelectric transition occurs between this acentric structure and a centric structure, that is from the ferroelectric to the paraelectric phase. Evidence for the onset of ferroelectricity can be found in the paraelectric phase Here V~.~.(O)and v,.,.(O) are the frequencies of the by studying the temperature variation of the static longitudinal and transverse optic modes with zero dielectric constant, ~(0).This follows a Curie-Weiss law wave number, ~(0)and ~(co)are the static and high frequency dielectric constants. Cochran and Cowley [4] have shown that, for a structure with n optic modes Conventional evidence for ferroelectricity clearly depends on the crystal being an insulator. No crystal with substantial conductivity could show any of the Cochran [27 argues that the lowest frequency transverse dielectric phenomena above, therefore no such crystal optic (T. 0.)mode is highly temperature dependent Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1968423 C 4 - 146 G. S. PAWLEY while all the other modes are relatively constant. Thus if the Curie-Weiss law, equation (I), is obeyed, this T. 0. frequency varies as Strontium titanate has a Curie temperature of 32 OK, and we are here interested in the phenomena in the cubic paraelectric phase. The exact nature of the transition or transitions is however still uncertain. The temperature dependence of the lowest T. 0. mode has been measured by Cowley [5] using the technique of neutron inelastic scattering and his measurements of the dispersion relation for the phonon branch with wave vectors along [loo] are shown in figure 1. FIG.2. -The temperature variation of the reciprocal of the static dielectric constant and the square of the frequency of the transverse optic mode of zero wave number for SrTiOs. crystal, containing only five atoms in the unit cell. Cochran [7] in studying PbTe, pointed out that there is in principle no reason why a diatomic ionic crystal should not have a ferroelectric transition Work on PbS and PbTe [8], both n-type extrinsic semiconductors with carrier concentrations of about 10'' crnF3, led to the study of SnTe, a p-type semiconductor with a much higher carrier concen- tration. All these substances have the NaCl structure, so it is instructive to compare their phonoa dispersion curves with those of KBr and NaI [9]. Figure 3 shows part of the measured dispersion curves for these Reduced wove vector 3 2z five crystals. This part, similar in each case, is sufficient FIG. 1. -The dispersion in the lowest transverse optic for our present purposes. Figure 3 (a) and (b) show branch of SrTiO3 for wave vectors along [loo] at 90 OK and KBr and NaI in which we see that the T. 0. branch 296 OK. THz a This contains results at two temperatures whereas 7 - figure 2 shows values of V;~(O)at a number of temperatures. Figure 2 also shows the variation of E(o)-' with temperature, as measured by Mitsui and Westphal [6], and the juxtaposition of these results 3- emphasies the simultaneous validity of equations (1) 2- and (4). Thus the appropriate temperature variation 1 - of the dielectric constant or the frequency of the n-- lowest T. 0.mode (the ferroelectric, soft or Cochran - - - - - mode) are equivalent evidence for a ferroelectric IReduced wave vector +om the origin to the zone boundary transition. FIG. 3. -The measured phonon dispersion curves for five crystals with the NaCl structure for wave vectors along [loo]. 2. Diatomic ferroelectrics. - For some years (a) KBr at 90 OK, (b) NaI at 100 OK, (c) PbS at 296 OK, (d) PbTe BaTi03 has been the simplest known ferroelectric at 296 OK, (e) SnTe at 100 OK. EVIDENCE FOR FERROELECTRICITY IN IV-VI COMPOUNDS C4- 147 is flat in both cases. In contrast the T. 0. branches measurements would not quite become unstable for PbS, PbTe and SnTe (Fig. 3 (c), (d) and (e)) show against the T. 0. mode of vibration at absolute zero. a marked drop as the wave vector tends to zero. This The phonon dispersion curve measurements are effect is most noticeable in SnTe and prompted ideal for use in the study of models for the forces in measurements at a number of temperatures [lo]. crystals, and the (( shell )) model has proved most The results are shown in figures 4 and 5 respectively. useful for ionic crystals 18, 93. This model is an extension of Born's model, taking into account the electronic polarisability of the ions. This model has provided a good fit with experiment for KBr and NaI but a progressively poorer fit for PbS, PbTe and SnTe. The effect of screening by the carriers in the last three crystals is seen (Fig. 3) in the drop in the longitudinal optic (L. 0.) branch frequency when the wave number is of the order of or less than the Thomas-Fermi screening length [8]. An attempt to modify the shell model to take account of the effect of screening on all the dispersioil branches has met with some success [I 11. 3. The a-GeTe transition. - It has been established that GeTe undergoes a phase transition, thought to be second order, from a cubic phase with the NaCl struc- ture above 670OK to a rhombohedra1 phase below this temperature [12]. The lower symmetry structure is known as a-GeTe. In addition GeTe and SnTe form a continuous range of solid solutions, and at each FIG. 4. -The dispersion3f the optic modes of vibration colnposition there is a definite transition temperature with wave vectors along [I001 in SnTe at various temperatures. which varies almost linearly with composition. Extra- polation to pure SnTe gives a transition temperature about 0 OK which is not inconsistent with the lattice dynamical evidence. Arguing from the phonon dispersion curve measu- rements we could have predicted the crystal structure of a-GeTe. In a mode of vibration at zero wave num- ber all the atoms of one chemical species are moving in unison, and for the optic mode both species are moving in opposition.
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